Continuous lattice effect algebras admitting order-continuous states

Fuzzy Sets and Systems

Volumn 136, Issue 1, 2003, Pages 41-54

  Riečanová, Zdenka ^a  

^a SLOVAK UNIVERSITY OF TECHNOLOGY   (Slovakia)

Author keywords

Effect algebras; MV algebras states; Nonclassical logics; Order continuity; Valuations

Indexed keywords

FINITE ELEMENT METHOD; FORMAL LOGIC; FUZZY SETS; QUANTUM THEORY; THEOREM PROVING;

NONCLASSICAL LOGICS;

ALGEBRA;

EID: 0345352840     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-0114(02)00141-0     Document Type: Article

References (29)

1. Chang C.C. Algebraic analysis of many-valued logics. Trans. Amer. Math. Soc. 88:1958;467-490.
2. Cignoli R., D'Ottaviano I.M.L., Mundici D. Algebraic Foundations of Many-valued Reasoning. 2000;Kluwer Academic Publishers, Dordrecht.
3. A. Dvurečenskij, S. Pulmannová, New Trends in Quantum Structures, Kluwer Academic Publishers, Dordrecht, Boston, London and Ister Science, Bratislava, 2000.
4. Erné M., Riečanová Z. Order-topological complete orthomodular lattices. Topology Appl. 61:1995;215-227.
5. Foulis D., Bennett M.K. Effect algebras and unsharp quantum logics. Found. Phys. 24:1994;1331-1352.
6. Grätzer G. General Lattice Theory. 2nd Edition:1998;Birkhäuser Verlag, Basel, Boston, Berlin.
7. Greechie R.J. Orthomodular lattices admitting no states. J. Combin. Theory A. 10:1971;119-132.
8. Greechie R.J., Foulis D., Pulmannová S. The center of an effect algebra. Order. 12:1995;91-106.
9. Hájek P. Mathematics of Fuzzy Logic. 1998;Kluwer Academic Publishers, Dordrecht.
10. Höhle U., Klement E.P. Non-classical Logics and their Applications to Fuzzy Subsets. 1995;Kluwer Academic Publishers, Dordrecht.
11. Jenča G. Blocks of homogeneous effect algebras. Bull. Austral. Math. Soc. 64:2001;81-98.
12. Jenča G., Riečanová Z. On sharp elements in lattice ordered effect algebras. BUSEFAL. 80:1999;24-99.
13. Kalmbach G. Orthomodular Lattices. 1983;Academic Press, London.
14. Kaplansky I. Any complemented complete modular lattice is continuous geometry. Ann. Math. 61:1995;254-541.
15. H. Kirchheimová, Z. Riečanová, Notes on order convergence and order topology, Appendix B, in: B. Riečan, T. Neubrunn (Eds.), Integral, Measure and Ordering, Kluwer Academic Publishers, Dordrecht and Ister Science, Bratislava, 1997.
16. Kôpka F. D-posets of fuzzy sets Tatra Mt. Math. Publ. 1:1992;83-87.
17. Kôpka F., Chovanec F. Boolean. D-posets Internat. J. Theor. Phys. 34:1995;1297-1302.
18. Pták P., Pulmanová S. Orthomodular Structures as Quantum Logics. 1991;Kluwer Academic Publishers, Dordrecht, Boston, London.
19. Riečan B., Neubrunn T. Integral, Measure and Ordering. 1997;Kluwer Academic Publishers, Dordrecht and Ister Science, Bratislava.
20. Riečanová Z. Topological and order-topological orthomodular lattices. Bull. Austral. Math. Soc. 47:1993;509-518.
21. Riečanová Z. On order continuity of quantum structures and their homomorphisms. Demonstratio. Math. 29:1996;433-443.
22. Riečanová Z. Order-topological separable complete modular ortholattices admit order continuous faithful valuations. Proc. Amer. Math. Soc. 126:1998;231-237.
23. Riečanová Z. Strongly compactly atomistic orthomodular lattices and modular ortholattices. Tatra Mt. Math. Publ. 15:1998;143-153.
24. Riečanová Z. Subalgebras, intervals and central elements of generalized effect algebras. Internat. J. Theor. Phys. 38:1999;3209-3220.
25. Riečanová Z. Compatibility and central elements in effect algebras. Tatra Mt. Math. Publ. 16:1999;151-158.
26. Riečanová Z. Generalization of blocks for. D-lattices and lattice ordered effect algebras Internat. J. Theor. Phys. 39:2000;231-237.
27. Riečanová Z. Lattice effect algebras with (o)-continuous faithful valuations. Fuzzy Sets and systems. 124:2001;321-327.
28. Riečanová Z. Orthogonal sets in effect algebras. Demonstratio. Math. 34:2001;525-532.
29. Riečanová Z., Bršel D. Contraexamples in difference posets and orthoalgebras. Internat. J. Theor. Phys. 23:1994;133-141.